International Journal of Innovative
Computing, Information and Control
Volume 17, Number 3, June 2021c
ICIC International ⃝2021
ISSN 1349-4198
pp. 1055–1065

IMPACT OF REMOVAL STRATEGIES OF STAY-AT-HOME ORDERS
ON THE NUMBER OF COVID-19 INFECTORS AND PEOPLELEAVING THEIR HOMES
Yuto Omae1 , Yohei Kakimoto1 , Jun Toyotani1 , Kazuyuki Hara1
Yasuhiro Gon2 and Hirotaka Takahashi31College of Industrial Technology
Nihon University
1-2-1, Izumi, Narashino, Chiba 275-8575, Japanoomae.yuuto@nihon-u.ac.jp
2

Nihon University School of Medicine
30-1, Kami, Ooyaguchi, Itabashi, Tokyo 173-8610, Japan
3

Research Center for Space Science
Advanced Research Laboratories
Tokyo City University
8-15-1, Todoroki, Setagaya, Tokyo 158-0082, Japanhirotaka@tcu.ac.jp

Received January 2021; revised April 2021
Abstract. As of November 2020, the COVID-19 pandemic continues to rage across theworld. One of the measures that has been taken to curb the spread of the virus is blanket
stay-at-home orders. Staying at home signiﬁcantly limits close contact with others andcan, thus, decrease the number of new cases. However, if people refrain from going out,
this will cause signiﬁcant economic damage. For this reason, some people think that theseorders should be revoked after a short period of time, and people should get out more often. However, if blanket stay-at-home restrictions are lifted before a signiﬁcant decrease
is seen in the number of new cases, the number of infected people is likely to increase
within a short period. This will, in turn, hasten the next round of blanket stay-at-homeorders and lead to a further reduction in people who can leave their home. Against thisbackdrop, this study examines below phenomena, through a multi-agent simulation. The
early removal strategies of stay-at-home orders for increasing the number of people leaving their homes have the eﬀect of both increasing and decreasing the number of suchpeople. Therefore, we consider the strategies do not lead to a suﬃcient increase in theoverall number of people leaving their homes. To examine these phenomena, we conducted the simulations that consist of six scenarios with the diﬀerent removal condition of
stay-at-home orders. As a result, we could conﬁrm that when more removal conditionsof stay-at-home orders were eased, the tendencies of more number of infected people anddeath people were increasing with some exceptions. In contrast, there were almost nodiﬀerences among the numbers of people leaving their home of these scenarios. Based on
the results, we also examined the possibility of a strategy that covers both infected people
and the number of people allowed to leave their homes.
Keywords: COVID-19 infection, Blanket stay-at-home orders, Declared state of emergency, Multi-agent simulation

1. Introduction. The COVID-19 pandemic is spreading across the globe in November
2020. Particularly in Japan, the virus has infected 140,000 people in total and killed
more than 2,000 people as of November 30, 2020 [1]. For this reason, Japan has imposed
DOI: 10.24507/ijicic.17.03.1055

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Y. OMAE, Y. KAKIMOTO, J. TOYOTANI ET AL.

a variety of measures. One such measure is the blanket stay-at-home order that was
introduced after the country declared a state of emergency (imposed: April 7, 2020;
lifted: May 25, 2020). This was a blanket call from the government for citizens to stay athome. The number of domestic conﬁrmed cases reported in the week prior to the declaredstate of emergency was 300 per day, whereas the number reported the week right after
was ∼ 40 per day [2]. This allows us to conclude that blanket stay-at-home orders have
had a signiﬁcant eﬀect on reducing the number of new cases.
However, stay-at-home orders imply that people do not go shopping, eat outside, andtravel, thus causing major economic losses to the society as a whole. As the length of timeof the blanket stay-at-home restrictions increases, society’s demand for the removal of therestrictions is expected to increase. In such a case, we can speculate that the number of
new cases will increase at a relatively faster pace. This means that the period whereinpeople are required to stay at home again will be earlier. Therefore, removing the blanket
stay-at-home restrictions at an early stage may have the eﬀectiveness of decreasing thenumber of people leaving their home – or increasing it.
It is diﬃcult to assess whether this phenomenon could actually take place in modern
society. In such a case, it is necessary to conduct simulations for veriﬁcation. As previous
researches, there are many cases developing virus infection simulators [3, 4, 5, 6]. By
following these ﬁndings, the development of COVID-19 simulators that model infection
transmission rates could be performed at a comparatively early stage. Examples include
Hou et al. [7] for Wuhan, China, Prasse et al. [8] and Yang et al. [9] for Hubei, China,
Chatterjee et al. [10] for India, Achterberg et al. [11] for Holland, and Liu et al. [12],for South Korea, Italy, and France. Moreover, Albahar et al. [13] conducted COVID-19
simulations with USA, Saudi Arabia and China using the ensemble machine learning.
From these previous researches, it was clariﬁed that the measures to isolate those infectedwith COVID-19 eﬀectively reduce the number of infected people at the peak hours [7]and that city blockades can reduce the damage caused by infection by 90% [10]. In termsof assessing other beneﬁts, Kurahashi [14] reported that working from home, staggered
commuting self-isolation at home when running a fever, and other such measures wereeﬀective in reducing the number of new cases. Niwa et al. [15] reported that quarantining
travelers at airports reduced the number of new cases by 90%. Certain studies also
assessed the eﬀectiveness of apps that notify users if they have been in contact withpeople infected with COVID-19 [16, 17, 18, 19, 20, 21]. Additionally, Yang et al. [22] andHe et al. [23] have conducted COVID-19 infection transmission simulations. These results
have enabled us to clarify the trends toward growth and suppression of the COVID-19
infection.
Thus far, these studies have focused on predicting the number of infected people andverifying the eﬀectiveness of some measures on decreasing new infectors. Although these
focuses are important, we consider increasing the number of people leaving their home isalso important from the view point of economic activity. However, these previous studies
did not evaluate the number of people leaving their home. Therefore, in this study, wetake up stay-at-home orders which is one of measures and evaluate the eﬀects on thenumber of infected people and people leaving their home. In particular, we use a multiagent simulation (MAS) to verify whether the phenomenon occurs, in which “the strategy
for early removal of blanket stay-at-home orders, for the purpose of increasing the numberof people leaving the home is, when viewed from a long-term perspective, not eﬀective
in suﬃciently increasing the number of people leaving the home”. Following this, we
present several strategies, including strategies for removing blanket stay-at-home orders
after the number of new cases has suﬃciently decreased, and we investigate the impact
these strategies have on the number of new cases and the number of people going out.

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Based on the results, we make some observations on the nature of the strategies proposedthat help reduce the number of new cases while allowing a certain number of people togo out.
The construction of remaining sections is as follows. In Section 2, we brieﬂy describe
the simulation system used in this research. In Section 3, the objective, outline, the resultand discussion of the experiment are explained, respectively. Section 4 is devoted to thesummary and future work.
2. Simulator.
2.1. Daily flow. In this study, we estimate the transmission of COVID-19 infection using
MAS. An overview is shown in Figure 1. The simulation is performed in plane spaces(minimum 0, maximum 1,000) with axes of x-y. These include four types of facilities:
homes, companies, shops, and schools. Multiple facilities for each type are allowed. Home
refers to the place of residence of the agent together with three other people: an oﬃce
worker, a homemaker and a student. The agents, who set oﬀ from home, will, based ona probability, move to their destination facility at a predetermined time. The respective
destinations are the company for the oﬃce worker, shops for the homemaker and school forthe student. The agents that move along the shortest path, in terms of actual distance,
can remain only for a certain amount of time that is determined by the above-statedprobability. After that certain amount of time, they return home, taking the shortest
path based on Euclidean distance. The above describes the processing ﬂow for one day.
This simulator uses one (1) step for every 10 minutes and moves to the next day once 24
hours (144 steps) have been completed. The simulation ends when it reaches the set time.
The processes were proposed as previous research (In detail, see Section 2.2 in [20]).

Figure 1. Constructed artiﬁcial society
2.2. Infection state transition. The MAS constructed in this study aims to simulate
the virus infection transmission. For this reason, each agent has an infection state parameter. These are the ﬁve states – S, E, I, R, and D – as described below. The states
were determined with reference to the SEIR (Susceptible, Exposed, Infectious, Recovered)model [22, 23] that simulates the COVID-19 infection transmission. “S: susceptible” isthe state in which the agent has never been infected with the virus. As the agent is not
immune, it has a likelihood of being infected. “E: exposed” is the state in which theagent is infected but is not yet symptomatic (latent period). “I: infectious” is the state inwhich the agent is infected and the symptoms have appeared (symptomatic period). “R:recovered” is the state in which the agent recovers after having been symptomatic. “D:death” is the state in which the agent did not recover and died.
The infection state transitions in the SEIR model are shown in Figure 2. The agent in
the S state transforms to the E state, according to whether they have come into contact

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Figure 2. SEIR modelwith an infected person. The deﬁnition of contact with an agent and infected personmeans that each other’s Euclidean distance is under 1. It is possible to set whether infected
people that can infect others are only those who are in the I state or whether those in the
E state are also included. This means that it is possible to express infectiousness during
the symptomatic state (I) and/or the latency state (E). An agent who has transformed
from the S to the E state also transforms to the I state as time passes. Agents in the I
state transform to the R or the D state as time passes. The question of whether patientstransform to the R or the D state depends on the fatality rate of the cases. The numericalmodels of the state transitions mentioned here are described in Section 2.1 in [20].
2.3. Small scale network. As this simulator aims to estimate the virus infection transmission, the contact between agents has considerable weight. Despite considering a contact has been made when the Euclidean distance in the plane space is below a threshold(each other’s Euclidean distance is under 1), this condition detaches the situation fromreality. In this study, each facility (i.e., a company or a school) is managed as one coordinate, so all agents arriving at the facilities are in contact with one another from a
Euclidean distance perspective. Therefore, even if there is one infected person among
them, there is a risk that this person will infect all of the agents. However, in the realworld, people work in company in separate departments, and in schools students taketheir lessons in their respective classrooms. Therefore, it is unlikely that everyone in thesame facility would come into contact with each other in a day. However, in the case oflong time simulation, we consider everyone would come into contact with each other inthe same facility, indirectly.
To express this with MAS, it is necessary to assume that the agents gathered in one facility are divided into multiple subgroups and only those within each group are considered
to come into contact with each other. For this reason, we have implemented the conceptof a small scale network (SSN) on the simulator in our study. An image of this simulator
is shown in Figure 3. This expresses the fact that there are 14 agents in this company;
these are divided into 3 SSNs. Whereas all 14 are in the same coordinates in the plane
space, only the agents in the same SSN come into contact with each other. Therefore,
the risk of infection exists only when there are infected persons within the same SSN.
When we incorporate the concept of SSNs within the simulator, it is necessary to havethe maximum SSN size parameter. This describes the maximum number of agents thatcan exist within one network (in the example in Figure 3, this is ﬁve people). The agentsare allocated to their respective SSN based on the order of arrival. Particularly, they
are initially allocated to SSN1 and when the maximum size is reached, SSN2 is created,
and this allocation processing is repeated. As the time at which each agent leaves homedepends on probability, the order of their arrival to the facility is random. Therefore, theassigned SSN is random every day. The concept of judging whether contact has been established based on the allocated SSN is only introduced to the outside facility (company,

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Figure 3. Small scale network
shop, or school). When agents are moving between the facility and their home, judging
whether contact has been established is only based on Euclidean distance.
2.4. Blanket stay-at-home orders. Next, we would like to discuss the blanket stayat-home orders for all agents. To express these, we need to prepare the three parametersof start conditions, removal conditions and restriction levels on going out. The standard
for starting blanket stay-at-home orders is the number of symptomatic agents (number of
agents in the I state) at the present time. Therefore, both the start and removal conditions
are values that represent the agent in the I state. When the number of agents in the I statemeets or exceeds the start condition, a blanket stay-at-home order is issued. Furthermore,when the number of agents in the I state falls below the removal condition, the blanket
stay-at-home restriction is removed. In Section 2.1, we explained that agents go out
every day. However, some agents do not go out, because all agents have the parameterof probability of leaving home, which is the probability of moving from their homes totheir destination facilities (company, shop, or school). During the time that the blanket
stay-at-home order is in place, the probability of leaving home of all agents decreases by
the set of restriction levels on going out. For example, if the probability of leaving homeis 100% and the restriction levels on going out is 90%, the probability of moving fromtheir homes to their destination facilities during the blanket stay-at-home order is 10%.
As it is diﬃcult for all agents (including the I state) to leave their home, the probability
the virus spreads in the companies, shops, and schools decreases, and it becomes easier
to maintain the S state agent status. For this reason, by executing a stay-at-home order,
it is possible to reduce the number of infections.
3. Experiment.
3.1. Purpose and overview. To eﬀectively operate society during the protracted periodof COVID-19 spread, it is necessary to not only reduce the total number of infections but
also keep (or increase) the number of people leaving home. In this study, we investigate
the impact of the strategy of blanket stay-at-home orders, which is one measure forsuppressing the spread of COVID-19 infection on the total number of infections andnumber of people leaving their home. The strategy to be veriﬁed on this occasion isshown in Table 1. The stay-at-home order is issued when the number of agents in the I
state meets or exceeds the number set in the start conditions, and the stay-at-home orderis removed when the number falls below the number set in the removal conditions.
During the stay-at-home order, the rate of all agents going out is lowered according
to the level of restrictions on going out. The start conditions, removal conditions andlevel of restrictions on going out are all important parameters, and on this occasion,
the start conditions were ﬁxed at 60 people and the level of restrictions on going out at
90%, with only the removal conditions variable. For strategy 0, the removal conditions

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Y. OMAE, Y. KAKIMOTO, J. TOYOTANI ET AL.

Table 1. Strategy for stay-at-home orders. Start conditions: when thenumber of people in the I state reaches a set number or above, a stay-athome order is issued. Removal conditions: when the number of people in
the I state is below a set number, the stay-at-home order is removed.
Strategy ID Start cond. [people] Removal cond. [people]
Strategy 0
Strategy 1
Strategy 2Strategy 3
Strategy 4
Strategy 5

60
60
60
60
60
60

5
10
20
30
40
50

Level of restriction
on going out [%]
90
90
90
90
90
90

were ﬁve people, and this means a return to normal life after the infection rate had
suﬃciently weakened following the issue of the stay-at-home order. As the number ofstrategies increases, the conditions for removal become more lenient. Strategy 0, in which
the removal conditions are strict, focuses on the social demand to reduce the number of
infections, whereas strategy 6, in which removal conditions are set to the largest value,stresses society’s demand for people to quickly return to normal life. We simulated eachstrategy and analyzed the impact on the total number of infections and the number ofpeople going out. When the simulation ends, the strategy with the lowest number of total
infections and the highest number of people leaving the home is considered the desirablesocial operation strategy under the prolonged spread of COVID-19.
The other simulator conditions are shown in Table 2. The total simulation period
was set to 365 days (1 calendar year). As there are 2,000 households and three agents
per household (oﬃce worker, homemaker, student), the total number of agents in theentire space is 6,000 (the reason that the start conditions for the aforementioned blanket
stay-at-home order were set to 60 people, so that it was a number comprising 1% of allagents).
Of these, ﬁve people were in I state, whereas the remaining 5,995 people were registeredin S state. The destination facilities of the agents leaving the house were allocated as
10 each of companies, shops, and schools. The maximum SSN size was set to a value
comprising an average of ﬁve networks per facility. There were 2,000 oﬃce workers,
housewives/househusbands and students within the 10 companies, shops, and schools,
respectively. Therefore, there were a maximum of 200 agents in each facility. Dividing
this value by 5 gives us 40 agents, so the maximum SSN size is 40 people. Other items,
such as EI state transition period (period for transitioning from E to I state), IRD statetransition period (period from transitioning from I to R or D state), rate at which agent
leaves the home, departure time, and stay time, were determined with reference to Omae
et al. [20]. The infection probability (probability of moving from S to E state aftercoming into contact with a latent or symptomatic agent for 10 minutes) is not clear fromthe COVID-19 infection rate, so the value at which infection is high to some extent issearched for by trial and error, and 0.030% was adopted.
3.2. Results and observations. The time-series ﬂuctuation in infections (latent casesand symptomatic cases) in relation to the executed simulation is shown in Figure 4.
The six graphs show the results when adopting the six strategies deﬁned in Table 1,
respectively. In this investigation, the only variable parameter among those specifying
the blanket stay-at-home order strategy is the removal condition. Although, for all of

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Table 2. Simulation conditions
Parameters
Simulation period
No. of households
Initial number of symptomatic agents
No. of facilities (company)
No. of facilities (shop)
No. of facilities (school)
Maximum SSN size
Probability of leaving home (oﬃce workers)
Probability of leaving home (homemaker)
Probability of leaving home (students)
Departure time (oﬃce workers)
Departure time (homemaker)
Departure time (students)
Stay time (oﬃce workers)
Stay time (homemaker)
Stay time (students)
Infection probability in the case of having contact
with infector
State in which infectors infect others
Fatality rate
Transition period from E to I
Transition period from I to R or D

Values365 [days]
2000 [households] (6000 [agents])
5 [agents]
10 locations*
10 locations*
10 locations*
40 [agents]
99.0∼100.0 [%]50.0∼100.0 [%]99.0∼100.0 [%]8:30±1:30
10:30±1:30
10:30±1:30
6:00∼8:00
0:10∼0:30
5:00∼6:00
0.030 [%]
I state, E state10.0 [%]
3, 5, 7 [days]
8, 10, 12 [days]*: coordinates are described in Appendix.
a∼b: uniform random number from a to b.
a±b: mean a, standard deviation b normal random number.

Figure 4. Time-series ﬂuctuation in latent cases and symptomatic cases(E, I states) in relation to the strategy adopting a blanket stay-at-home
order

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Y. OMAE, Y. KAKIMOTO, J. TOYOTANI ET AL.

the strategies, a stay-at-home order was issued when the number of symptomatic agentsexceeded 60, it should be noted that as there are a large number of latent agents at thattime, the number of symptomatic agents does not start to decrease the instant the stayat-home order is issued, but rather the latent agents switch to becoming symptomatic
agents, and only after a certain increase in the number of symptomatic agents does thenumber start to decrease.
Strategy 0 is a strategy for removing the order after the number of symptomatic agentshas decreased suﬃciently. With this strategy, the number of symptomatic agents peaks
at 188 people, and this tends to be repeated in ﬁxed cycles. As we move to strategies
1, 2, 3, 4, 5, the blanket stay-at-home order removal conditions are relaxed. In accordancewith this, we can see a trend toward the cycles becoming shorter in relation to the timeseries ﬂuctuation of infections. As the only measure introduced in this simulation to
reduce infections is a blanket stay-at-home order, this means that stay-at-home orders
are repeated in short cycles. We can conﬁrm that the more number of days passed goes
into the second half, the lower the number of peak symptomatic agents, but this justmeans that the number of patients in the S state that can be infected has decreased andthat it has fallen into the state of herd immunity, which is something society as a wholeshould avoid. Moreover, we show the time-series ﬂuctuation in states S and D in Figure 5.
From Figure 5, we can understand that the number of state S is keeping high value andthe number of state D is small in the case of strategy 0 comparied with other strategies.

Figure 5. Time-series ﬂuctuation in states S and D in relation to thestrategy adopting a blanket stay-at-home order. Sn means strategy n.
To make quantiﬁable observations of these results, we derived several indicators, suchas infection transmission and stay-at-home orders. These results are shown in Table 3.
The total number of infections at the endpoint of the one-year simulation is the numberof agents in the E, I, R, and D states. In the case of valuing small, it means that moreagents (healthy people who have never been infected) are maintained in the S state. The
maximum peak number of people is the maximum value in relation to the number of agentsin the I state. The higher this value is, the higher the maximum number of symptomatic
agents, which means that medical services may be overwhelmed. The peak number refers
to the peak number of agents in the I state. The ﬁrst-half cycle and second-half cycle
are the ﬁrst half and second half of 365 days, respectively, and this refers to the cyclicalfeatures calculated from the power spectrum in relation to the time-series ﬂuctuationsof agents in the I state. The larger the peak number or the shorter the cycle, the more

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Table 3. The number of infections and number of people leaving the homein relation to the adopted strategy (total population: 6,000 people, total
period: 365 days)
Strategy ID*
S0
S1
S2
S3
S4
S5
Total number of infections [people/year]
1864 2330 2849 3184 3428 3561
Maximum number at peak [people/day]
188 211 238 276 344 363
Peak number [unit]
5
7
8
9
10
10
First-half cycle [days]
60
60
45
45
45
36
Second-half cycle [days]
60
60
45
36
36
30
Total number of death people [people/year] 169 231 290 285 343 333
Average number of people leaving the home1917 2054 2000 1958 2055 2183
[people/day]
Stay-at-home order days [days]
255 246 250 253 246 236*: Refer to Table 1 for strategy. Sn means strategy n.

times the medical services are likely to be overwhelmed, which means that stay-at-homeorders will occur frequently. The average number of people leaving their home refers
to the average number of people leaving their home per day in the one-year simulation.
The number of stay-at-home days refers to the number of days covered by stay-at-homeorders during the one-year simulation. The larger the average number of people leaving
the house is, or the smaller the number of days covered by stay-at-home orders, the more
active people are moving, so this means that economic problems are less likely to occur.
When looking at this, we can conﬁrm that the more the removal conditions for blanket
stay-at-home orders are eased, the tendencies of the more the total number of infections
and death people, maximum peak number of people, and peak number increase, and theshorter the time-series ﬂuctuation cycle for agents in the I state. However, there are also
exceptions, e.g., the number of death people of S2 is higher than S3 and that of S4 ishigher than S5. On the contrary, even if the removal conditions are eased, we can conﬁrm
that this does not greatly impact the average number of people leaving their home or
the number of days covered by the stay-at-home order. As people can immediately leave
their home when the removal conditions are eased, it can lead to an increased numberof people leaving the home. However, even if the blanket stay-at-home order is released
before the number of symptomatic agents has suﬃciently decreased, it will have the eﬀect
of increasing the number of symptomatic agents immediately; thus, hastening the next
stay-at-home order will lead to reduction in the number of people who can leave the home.
As these conﬂict with each other, it is considered that the number of people leaving thehouse does not clearly increase even if the removal conditions are relaxed.
Normally, the motivation for removing blanket stay-at-home orders at an early stage
comes from a desire to revitalize the movement of people and restart the economy. However, it has been conﬁrmed that if a strategy is adopted such that a blanket stay-at-homeorder is removed before the number of symptomatic agents has fallen suﬃciently, thenumber of infections will be increased. In such cases, not only will the potential for andfrequency of the medical services being overwhelmed increase, but also this will also do
not have a clear eﬀect in terms of increasing the number of people leaving the house. From
the above, we can see that when aiming for appropriate social operations during the timethat COVID-19 is spreading, it is important from the perspectives of both number of
infections and number of people leaving the home to adopt the strategy of not removing
the blanket stay-at-home orders until the number of symptomatic agents has suﬃciently
decreased.

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Y. OMAE, Y. KAKIMOTO, J. TOYOTANI ET AL.

4. Conclusion. In this study, we used an MAS expressing infection transmission andanalyzed the impact of the removal strategies for blanket stay-at-home orders on thenumber of infections and number of people leaving the home. We conﬁrmed from theresults that if blanket stay-at-home orders are removed at an early stage, not only the
number of infections greatly will increase and the potential for medical services to be
overwhelmed increase but also the speed of this cycle will be increased and the numberof people leaving the home will not suﬃciently increase. Particularly, if blanket stayat-home orders are removed at an early stage based on the idea of restarting economic
activity, society may be plunged into a major state of confusion. Therefore, if a blanket
stay-at-home order is issued, it is important to remove blanket stay-at-home orders only
after the number of infections has reduced suﬃciently.
Moving forward, we plan to validate the eﬀectiveness not only of blanket stay-at-homeorders but also a variety of other measures, such as the COVID-19 contact check app
COCOA, the avoidance of close contact with other people, and the expansion of medical
resources, as well as conduct a more detailed study on the kind of strategy that can beeﬀective in terms of both number of infections and number of people able to leave thehome.
Acknowledgment. This work was supported in part by the Telecommunications Advancement Foundation (Y. Omae, No. 20203002) and JSPS Grant-in-Aid for ScientiﬁcResearch (C) [J. Toyotani, 21K04535].
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Appendix. The (x, y) coordinates of companies, shops and schools in artiﬁcial society
are Lcompany = {(x, y) = (100, 100n)|n = 0, . . . , 9}, Lshop = {(x, y) = (500, 100n)|n =0, . . . , 9} and Lschool = {(x, y) = (900, 100n)|n = 0, . . . , 9}, respectively.